Alarm systems are known in which two or more sensors are embodied with associated logic circuits to achieve false alarm rates which are substantially less than the rates of a system employing a single sensor. Such redundant or multiple alarm systems for providing false alarm reduction are described for example in U.S. Pat. Nos. 3,074,053 and 3,074,054, assigned to the assignee of this invention. In such redundant sensor systems, an alarm output is provided only upon actuation of two or more sensors within a predetermined time interval. The probability that the multiple sensors will false alarm within the same time interval is very small compared to the probability of a false alarm of any single sensor. In many alarm system installations, it is desirable to provide an alarm output when any sensor of a plurality of sensors is actuated, to provide increased detection even though the false alarm rate will increase.